Facebook is doing a limited test of ads on mobile websites and mobile applications, displaying ads to people who are logged into Facebook.

So, if you are logged into Facebook on ESPN, and you head over to ESPN's mobile site, you might see an ad for Domino's Pizza.

That ad won't say that your buddy Nicholas loves Domino's, though: According to a Facebook rep, these ads won't have the "social context" that ads on Facebook's own website show.

An ad network could be a lucrative new source of revenue for Facebook.

But the ad-network space on the Web is incredibly crowded and competitive, with Google dominating the business.

The mobile-ad space is just getting started. And Facebook has a lot of data on users—not just demographic information, but the apps they use, and the apps their friends use.

One pool of customers for a Facebook mobile ad network: app developers who want to get more people to install their software.

Facebook is already selling ads on its own website and mobile apps that help encourage users to download new apps. Placing those ads on other Facebook-enabled apps and mobile websites could tap into big app-promotion budgets.

Local deals and e-commerce promotions are other logical categories that Facebook could exploit with a third-party ad network for mobile devices.

Update: We've corrected this story to note that Facebook's third-party ads won't display the names of users' friends, as Facebook's own ads do.